Having tried the once to cycle with it (and "it" is a resonator bass, perhaps I should have mentioned...), due to the angle of my back and length of bass etc I was unable to lift my head enough to see ahead comfortably. And on that occasion the seat clamp bolt attaching the saddle to the seatpost snapped and I fell off messily, brusing a rib. Whether the extra weight of the bass contributed to my accident or not I don't know, but I'm sure that if it hadn't been a steel one it would be in several pieces now.

If you've got pain, your body is telling you that you're doing something wrong. Take a look at your technique (preferably in a mirror) and eliminate anything that looks uncomfortable/awkward.

As for biking with a bass, I had no problems last year biking across town to my lessons with my bass on my back. One thing you could do is to get a bag that has really long backpack straps and lower it as far as you can without making the bag become tire fodder. If that doesn't work, I suggest getting a 2nd bass.

I say play the one that you're going to use for the rehearsals and gigs. No 2 basses play exactly the same. Even if they are the same model. You might find yourself making silly mistakes should you use one bass all week then break out a totally different one for a show.

If you use care while traveling, your bass will more than likely be fine. I don't care if its a $6000 Fodera or a $169 Yamaha RBX. If you treat it with the care it deserves by putting it inin at least a gig bag, then odds of something bad happening to it are greatly reduced.